发表机构
The Hong Kong University of Science and Technology; Institute of Physics, Chinese Academy of Sciences（香港科技大学; 中国科学院物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在任意图上精确求解电荷-4e 超导母体，严格证明无电荷-2e 凝聚的四重态 ODLRO，并给出仅含跳跃与两体相互作用的强耦合实现路径。
AI 中文摘要
直接电荷-4e 超导体展现出相干的四电子序，而所有电荷-2e 配对通道均未凝聚。我们建立了三个互补的结果。首先，基于 Yoshida 和 Katsura 的 η-团簇态与二分母体，我们在任意连通图上构造并精确求解了一个最小两项母体。其固定粒子数基态具有四重态非对角长程序（ODLRO）而无电荷-2e ODLRO，同时精确映射到经典硬核排斥动力学，得到完整固定扇区能隙和一支四重态密度模式。非零四重态刚度与消失的逆四重态压缩率将该 z=2 母体识别为相分离边界。其次，对于具有显式四重态转移和足够大在位惩罚的有限程费米子族，我们在半四重态填充下严格证明了四重态 ODLRO 而无电荷-2e ODLRO，既在 d≥2 的超立方 XY 点，也在方格上的有限 XXZ 区间内。第三，我们推导了仅使用电子跳跃和两体相互作用的强耦合实现。在位能隙 U0 下，配对跳跃 K 在 K^2/U0 阶产生四重态运动，而电子跳跃 t 首先在 t^4/U0^3 阶贡献；电荷-2e 激发保持 O(U0) 能隙。在二分格上，正的逆四重态压缩率开启了一个渐近可控的均匀 z=1 区域，具有短程对关联，而负曲率驱动相分离。
英文摘要
A direct charge-\(4e\) superconductor exhibits coherent four-electron order while every charge-\(2e\) pairing channel remains uncondensed. We establish three complementary results. First, building on the \(η\)-clustering states and bipartite parent of Yoshida and Katsura, we formulate and exactly solve a minimal two-term parent on any connected graph. Its fixed-number ground states have quartet off-diagonal long-range order (ODLRO) without charge-\(2e\) ODLRO, while an exact mapping to classical hard-core exclusion dynamics yields the full fixed-sector gap and a branch of quartet-density modes. Nonzero quartet stiffness and vanishing inverse quartet compressibility identify this \(z=2\) parent as a phase-separation boundary. Second, for a finite-range fermionic family with explicit quartet transfer and sufficiently large onsite penalty, we rigorously prove quartet ODLRO without charge-\(2e\) ODLRO at half quartet filling, both at the hypercubic XY point for \(d\geq2\) and throughout a finite XXZ interval on the square lattice. Third, we derive a strong-coupling realization using only electron hopping and two-body interactions. With local gap \(U_0\), pair hopping \(K\) generates quartet motion at order \(K^2/U_0\), whereas electron hopping \(t\) first contributes at order \(t^4/U_0^3\); charge-\(2e\) excitations remain gapped at \(O(U_0)\). On bipartite lattices, positive inverse quartet compressibility opens an asymptotically controlled homogeneous \(z=1\) regime with short-ranged pair correlations, while negative curvature drives phase separation.
Comments19 pages, 2 figures
